## Forward speed motions of a submerged body. The Cauchy problem.(English)Zbl 0568.35059

The linearized problem for the motion of a submerged body in a perfect, inviscid, irrotational fluid, occupying an unbounded domain of $$R^ 3$$, moving forward with a forced motion depending on (x,y) but not z, is $$\Delta u=0$$, $$u|_{\Sigma}=\phi$$, $$\partial u/\partial n|_{\Gamma}=f(t,\cdot)$$, and $$\phi_ t-a\cdot \phi_ x+w\cdot \phi_ y=-b\eta$$, $$\eta_ t-a\cdot \eta_ x+(w\cdot \eta)_ y=du/\partial n|_{\Sigma},$$ $$\phi |_{t=0}=\phi_ 0$$, $$\eta |_{t=0}=\eta_ 0$$. In this paper the elliptic and the initial- value problem are viewed as coupled by a pseudo-differential operator T. The Yosida approximation $$T^{\epsilon}$$ of T leads to a regularized initial-value problem. The perturbation theory of nonlinear semigroups is used to obtain weak solutions of the problem as $$\epsilon$$ goes to zero.
Reviewer: G.F.Webb

### MSC:

 35L45 Initial value problems for first-order hyperbolic systems 35J25 Boundary value problems for second-order elliptic equations 47H20 Semigroups of nonlinear operators 35D05 Existence of generalized solutions of PDE (MSC2000)
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